The unseeded British pair secured a Toyko quarter-final date with Croatians Marin Cilic and Ivan Dodig thanks to a 6-2 7-6 (7-2) victory over German duo Kevin Krawietz and Tim Puetz.
I’d have been annoyed with myself if I’d decided to play with the issue, made it worse, lost my singles and not been able to perform well in the doubles. Andy Murray
Andy Murray, 34, a two-time Games singles champion who withdrew from a third campaign in the individual event due to a thigh injury, said: “When we spoke about playing, I told Joe that if I had any physical issues I’d prioritise doubles over singles and that’s why I made the decision.
“I’d have been annoyed with myself if I’d decided to play with the issue, made it worse, lost my singles and not been able to perform well in the doubles.”
The victory kept Murray on course for a record-busting fourth Games medal, having claimed singles gold and, with Laura Robson, mixed doubles silver in 2012 and singles gold in 2016. Murray, who has made a stop-start comeback from hip trouble, would be the first male to win so many medals since tennis was re-introduced in 1988.
Former world No.1 Murray, twice Wimbledon champion, and Salisbury, who has lifted two major doubles titles, also scored a straight sets win when they stunned second seeds Nicolas Mahut and Pierre-Hugues Herbert, the French Open champions, in the opening round
Stefanos Tsitsipas, on a revenge mission, defeated American Frances Tiafoe, who stunned the Greek in the first round at Wimbledon, 6-3 6-4.
Diego Schwartzman and Jeremy Chardy also reached the last 16. Argentine Schwartzman saw off Tomas Machac of the Czech Republic 6-4 7-5. Frenchman Chardy battled to a 7-5 4-6 6-3 win over Asian Karasev of the Russian Olympic Committee.